XPM Prime Explorer symbol
XPMPrime Explorer

Block #187,244

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/30/2013, 10:21:34 AM Β· Difficulty 9.8677 Β· 6,621,466 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d58dc9386c8baee1508adc4c943f1b52a552418f4b8fa2fa18635498b7060385
View on Chainz β†—

Height

#187,244

Difficulty

9.867733

Transactions

1

Size

199 B

Version

2

Bits

09de23b9

Nonce

35,438

Timestamp

9/30/2013, 10:21:34 AM

Confirmations

6,621,466

Mined by

⛏️ P2SHAc8C5CfDASXvqVddePmQ2RQ39gSojGXosx

Merkle Root

e5a7370e101963a2e53c9a1b2de3a66f7e7b549059a82592eca589195e759f00
Transactions (1)
Coinbasee5a7370e101963…a589195e759f00
1 in β†’ 1 out10.2500 XPM109 B
Ac8C5CfD…SojGXosx
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.

3.813 Γ— 10⁹³(94-digit number)
38131894727473362360…21109751614661238399
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
3.813 Γ— 10⁹³(94-digit number)
38131894727473362360…21109751614661238399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.813 Γ— 10⁹³(94-digit number)
38131894727473362360…21109751614661238401
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
7.626 Γ— 10⁹³(94-digit number)
76263789454946724720…42219503229322476799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.626 Γ— 10⁹³(94-digit number)
76263789454946724720…42219503229322476801
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
1.525 Γ— 10⁹⁴(95-digit number)
15252757890989344944…84439006458644953599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.525 Γ— 10⁹⁴(95-digit number)
15252757890989344944…84439006458644953601
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
3.050 Γ— 10⁹⁴(95-digit number)
30505515781978689888…68878012917289907199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.050 Γ— 10⁹⁴(95-digit number)
30505515781978689888…68878012917289907201
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
6.101 Γ— 10⁹⁴(95-digit number)
61011031563957379776…37756025834579814399
Verify on FactorDB β†—Wolfram Alpha β†—

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 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 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 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:57,713,731 XPMΒ·at block #6,808,709 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