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Block #321,864

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/20/2013, 2:06:55 PM Β· Difficulty 10.1990 Β· 6,491,138 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fe718adb419efd181b857383989ddbeb8a13d1a1f9b3e3cca24637ee04b40a8b
View on Chainz β†—

Height

#321,864

Difficulty

10.199048

Transactions

1

Size

205 B

Version

2

Bits

0a32f4c9

Nonce

89,873

Timestamp

12/20/2013, 2:06:55 PM

Confirmations

6,491,138

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

97a3dd6d4e0b50e011c5271c3ec5aada750ad9908f5e9a06344447c05dadbd19
Transactions (1)
Coinbase97a3dd6d4e0b50…4447c05dadbd19
1 in β†’ 1 out9.6000 XPM116 B
AbwWkWZt…kawDhufa
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.

2.343 Γ— 10⁹³(94-digit number)
23434998900295239204…91708227601814092799
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
2.343 Γ— 10⁹³(94-digit number)
23434998900295239204…91708227601814092799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.343 Γ— 10⁹³(94-digit number)
23434998900295239204…91708227601814092801
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
4.686 Γ— 10⁹³(94-digit number)
46869997800590478409…83416455203628185599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.686 Γ— 10⁹³(94-digit number)
46869997800590478409…83416455203628185601
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
9.373 Γ— 10⁹³(94-digit number)
93739995601180956818…66832910407256371199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.373 Γ— 10⁹³(94-digit number)
93739995601180956818…66832910407256371201
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
1.874 Γ— 10⁹⁴(95-digit number)
18747999120236191363…33665820814512742399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.874 Γ— 10⁹⁴(95-digit number)
18747999120236191363…33665820814512742401
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
3.749 Γ— 10⁹⁴(95-digit number)
37495998240472382727…67331641629025484799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.749 Γ— 10⁹⁴(95-digit number)
37495998240472382727…67331641629025484801
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,748,056 XPMΒ·at block #6,813,001 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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