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Block #240,839

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/2/2013, 8:36:13 PM Β· Difficulty 9.9572 Β· 6,562,702 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1eb64e828e5375d21ae7a9fef2be024545e63e89057f9f026074a13a11dbdf2f
View on Chainz β†—

Height

#240,839

Difficulty

9.957222

Transactions

1

Size

199 B

Version

2

Bits

09f50c80

Nonce

396,706

Timestamp

11/2/2013, 8:36:13 PM

Confirmations

6,562,702

Mined by

⛏️ P2SHASeXJJsTuk2nKV74JiRd8kaBoaFfTkAVgb

Merkle Root

6c840de3287b23a5d86ec3249e41b759efda5de6cc28b482c6ccb0c81978bf0c
Transactions (1)
Coinbase6c840de3287b23…ccb0c81978bf0c
1 in β†’ 1 out10.0700 XPM109 B
ASeXJJsT…FfTkAVgb
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.

4.746 Γ— 10⁹³(94-digit number)
47463144969754824207…75691029107953391119
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
4.746 Γ— 10⁹³(94-digit number)
47463144969754824207…75691029107953391119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.746 Γ— 10⁹³(94-digit number)
47463144969754824207…75691029107953391121
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
9.492 Γ— 10⁹³(94-digit number)
94926289939509648415…51382058215906782239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.492 Γ— 10⁹³(94-digit number)
94926289939509648415…51382058215906782241
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
1.898 Γ— 10⁹⁴(95-digit number)
18985257987901929683…02764116431813564479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.898 Γ— 10⁹⁴(95-digit number)
18985257987901929683…02764116431813564481
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
3.797 Γ— 10⁹⁴(95-digit number)
37970515975803859366…05528232863627128959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.797 Γ— 10⁹⁴(95-digit number)
37970515975803859366…05528232863627128961
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
7.594 Γ— 10⁹⁴(95-digit number)
75941031951607718732…11056465727254257919
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:57,672,358 XPMΒ·at block #6,803,540 Β· updates every 60s
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