XPM Prime Explorer symbol
XPMPrime Explorer

Block #101,922

TWNLength 9ā˜…ā˜†ā˜†ā˜†ā˜†

Bi-Twin Chain Ā· Discovered 8/6/2013, 9:18:43 PM Ā· Difficulty 9.4773 Ā· 6,706,123 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
78e4cf5eceef959f2c1e3537891c143668e04c7f4c039112ecd17d0a46f126d7
View on Chainz ā†—

Height

#101,922

Difficulty

9.477251

Transactions

4

Size

3.78 KB

Version

2

Bits

097a2d1f

Nonce

244,768

Timestamp

8/6/2013, 9:18:43 PM

Confirmations

6,706,123

Mined by

ā›ļø P2SHANBzzanyqRvQeZ8m9JK69ZLmMMGoYzLtp4

Merkle Root

f42cb93d9232e733637d050c8e02a9c214460950462c50dace9321c9a06e0cf1
Transactions (4)
Coinbaseff8d4dd9c85122ā€¦dc45c3f4e1b42c
1 in ā†’ 1 out11.1700 XPM109 B
ANBzzanyā€¦GoYzLtp4
cece0f09bf1b94ā€¦445bb3d1a713e5
2 in ā†’ 2 out67.3710 XPM375 B
AHXRWc4Pā€¦7RKarvB8AYqTamKPā€¦YVd6pPgx
cc634515ce7de0ā€¦ecd60d4c945e6f
24 in ā†’ 1 out250.0000 XPM2.85 KB
AL3jCG2Kā€¦moye79K3
ca504907371d00ā€¦8f91864e671c62
2 in ā†’ 2 out2.8457 XPM373 B
ANNRX3ZSā€¦2JWfwghiAGeqHfHtā€¦G9meMD4L
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) ā€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

5.697 Ɨ 10ā¹ā“(95-digit number)
56970315894916405998ā€¦48743290338661679159
Discovered Prime Numbers
Lower: 2^k Ɨ origin āˆ’ 1 | Upper: 2^k Ɨ origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 ā€” Twin Prime Pair (origin Ā± 1)
origin āˆ’ 1
5.697 Ɨ 10ā¹ā“(95-digit number)
56970315894916405998ā€¦48743290338661679159
Verify on FactorDB ā†—Wolfram Alpha ā†—
origin + 1
5.697 Ɨ 10ā¹ā“(95-digit number)
56970315894916405998ā€¦48743290338661679161
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: origin + 1 āˆ’ origin āˆ’ 1 = 2 (twin primes āœ“)
Level 1 ā€” Twin Prime Pair (2^1 Ɨ origin Ā± 1)
2^1 Ɨ origin āˆ’ 1
1.139 Ɨ 10ā¹āµ(96-digit number)
11394063178983281199ā€¦97486580677323358319
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^1 Ɨ origin + 1
1.139 Ɨ 10ā¹āµ(96-digit number)
11394063178983281199ā€¦97486580677323358321
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: 2^1 Ɨ origin + 1 āˆ’ 2^1 Ɨ origin āˆ’ 1 = 2 (twin primes āœ“)
Level 2 ā€” Twin Prime Pair (2^2 Ɨ origin Ā± 1)
2^2 Ɨ origin āˆ’ 1
2.278 Ɨ 10ā¹āµ(96-digit number)
22788126357966562399ā€¦94973161354646716639
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^2 Ɨ origin + 1
2.278 Ɨ 10ā¹āµ(96-digit number)
22788126357966562399ā€¦94973161354646716641
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: 2^2 Ɨ origin + 1 āˆ’ 2^2 Ɨ origin āˆ’ 1 = 2 (twin primes āœ“)
Level 3 ā€” Twin Prime Pair (2^3 Ɨ origin Ā± 1)
2^3 Ɨ origin āˆ’ 1
4.557 Ɨ 10ā¹āµ(96-digit number)
45576252715933124798ā€¦89946322709293433279
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^3 Ɨ origin + 1
4.557 Ɨ 10ā¹āµ(96-digit number)
45576252715933124798ā€¦89946322709293433281
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: 2^3 Ɨ origin + 1 āˆ’ 2^3 Ɨ origin āˆ’ 1 = 2 (twin primes āœ“)
Level 4 ā€” Twin Prime Pair (2^4 Ɨ origin Ā± 1)
2^4 Ɨ origin āˆ’ 1
9.115 Ɨ 10ā¹āµ(96-digit number)
91152505431866249597ā€¦79892645418586866559
Verify on FactorDB ā†—Wolfram Alpha ā†—

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin ā€” the large number shown above ā€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

ā˜…ā˜†ā˜†ā˜†ā˜†
Rarity
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Ɨ 3 Ɨ 5 Ɨ 7 Ɨ ā€¦), the result is the first prime in the chain. The origin is deliberately divisible by this primorial ā€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Ɨ Primorial (2Ā·3Ā·5Ā·7Ā·11Ā·ā€¦)
Source: Primecoin prime.cpp ā€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors ā€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial āˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,708,405 XPMĀ·at block #6,808,044 Ā· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Ā·Privacy Policy