XPM Prime Explorer symbol
XPMPrime Explorer

Block #61,223

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/18/2013, 12:14:42 PM Β· Difficulty 8.9723 Β· 6,748,566 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d3138d307aa1c0411338eb20efcbde5ec42289e66a3c6730f77de14bc6b97785
View on Chainz β†—

Height

#61,223

Difficulty

8.972302

Transactions

1

Size

200 B

Version

2

Bits

08f8e8cf

Nonce

1,845

Timestamp

7/18/2013, 12:14:42 PM

Confirmations

6,748,566

Mined by

⛏️ P2SHAV6P7enUMtWL6sjxBf1aCsLJbsVLHeixvR

Merkle Root

735e70fa656066721d230e7dc1e272c16bacb49ff9862c60dec2f63869235e21
Transactions (1)
Coinbase735e70fa656066…c2f63869235e21
1 in β†’ 1 out12.4000 XPM110 B
AV6P7enU…VLHeixvR
Prime Chain Origin

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

3.592 Γ— 10⁹⁴(95-digit number)
35920273761115581230…69169975555118305819
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— 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 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
3.592 Γ— 10⁹⁴(95-digit number)
35920273761115581230…69169975555118305819
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.592 Γ— 10⁹⁴(95-digit number)
35920273761115581230…69169975555118305821
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
7.184 Γ— 10⁹⁴(95-digit number)
71840547522231162461…38339951110236611639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.184 Γ— 10⁹⁴(95-digit number)
71840547522231162461…38339951110236611641
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
1.436 Γ— 10⁹⁡(96-digit number)
14368109504446232492…76679902220473223279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.436 Γ— 10⁹⁡(96-digit number)
14368109504446232492…76679902220473223281
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
2.873 Γ— 10⁹⁡(96-digit number)
28736219008892464984…53359804440946446559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.873 Γ— 10⁹⁡(96-digit number)
28736219008892464984…53359804440946446561
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 8 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜†β˜†β˜†β˜†
Rarity
CommonChain length 8

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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” 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 βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,722,393 XPMΒ·at block #6,809,788 Β· 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.

Β·Privacy Policy