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Block #18,628

TWNLength 7β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/12/2013, 6:00:54 AM Β· Difficulty 7.9110 Β· 6,787,966 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
87b8a1843f1e16f89892d76ac5815b7a58bc40bd8a8179f029516f37169ea0a2
View on Chainz β†—

Height

#18,628

Difficulty

7.910988

Transactions

1

Size

199 B

Version

2

Bits

07e93684

Nonce

212

Timestamp

7/12/2013, 6:00:54 AM

Confirmations

6,787,966

Mined by

⛏️ P2SHAWMteqdVMhAhAkUuUfnMnzfAFbsGWCn49w

Merkle Root

056dc67af6d02b725a1a9e28811fc3bfe87d8dd1a876969fca72bfa565ecf8ef
Transactions (1)
Coinbase056dc67af6d02b…72bfa565ecf8ef
1 in β†’ 1 out15.9600 XPM108 B
AWMteqdV…sGWCn49w
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.

3.155 Γ— 10⁹⁷(98-digit number)
31550734072056209143…00954644167703713789
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
3.155 Γ— 10⁹⁷(98-digit number)
31550734072056209143…00954644167703713789
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.155 Γ— 10⁹⁷(98-digit number)
31550734072056209143…00954644167703713791
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
6.310 Γ— 10⁹⁷(98-digit number)
63101468144112418287…01909288335407427579
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.310 Γ— 10⁹⁷(98-digit number)
63101468144112418287…01909288335407427581
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
1.262 Γ— 10⁹⁸(99-digit number)
12620293628822483657…03818576670814855159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.262 Γ— 10⁹⁸(99-digit number)
12620293628822483657…03818576670814855161
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
2.524 Γ— 10⁹⁸(99-digit number)
25240587257644967314…07637153341629710319
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 7 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 7

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:57,696,850 XPMΒ·at block #6,806,593 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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