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Block #256,032

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/11/2013, 2:12:23 PM Β· Difficulty 9.9751 Β· 6,558,283 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
bb3349000aa94320c04a3ce101644e789516b2e3d3d245ff573e5a3a54d2c5dd
View on Chainz β†—

Height

#256,032

Difficulty

9.975070

Transactions

1

Size

199 B

Version

2

Bits

09f99e35

Nonce

52,967

Timestamp

11/11/2013, 2:12:23 PM

Confirmations

6,558,283

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

775c76d7ad6929868fb79651f002d8b1cc51498a132b9fe5bd801a1f04bafce3
Transactions (1)
Coinbase775c76d7ad6929…801a1f04bafce3
1 in β†’ 1 out10.0300 XPM110 B
AeKNrjNj…1NEq95Ta
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.

2.309 Γ— 10⁹³(94-digit number)
23097972539528219942…83536605830541797439
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
2.309 Γ— 10⁹³(94-digit number)
23097972539528219942…83536605830541797439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.309 Γ— 10⁹³(94-digit number)
23097972539528219942…83536605830541797441
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
4.619 Γ— 10⁹³(94-digit number)
46195945079056439885…67073211661083594879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.619 Γ— 10⁹³(94-digit number)
46195945079056439885…67073211661083594881
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
9.239 Γ— 10⁹³(94-digit number)
92391890158112879771…34146423322167189759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.239 Γ— 10⁹³(94-digit number)
92391890158112879771…34146423322167189761
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
1.847 Γ— 10⁹⁴(95-digit number)
18478378031622575954…68292846644334379519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.847 Γ— 10⁹⁴(95-digit number)
18478378031622575954…68292846644334379521
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
3.695 Γ— 10⁹⁴(95-digit number)
36956756063245151908…36585693288668759039
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:57,758,583 XPMΒ·at block #6,814,314 Β· updates every 60s
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