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Block #181,980

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/26/2013, 11:09:35 PM Β· Difficulty 9.8596 Β· 6,621,384 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
213ae9eb133ebbec9cf2a3d2977804c1ba735ed7d30c44277502c5b3b89aef5e
View on Chainz β†—

Height

#181,980

Difficulty

9.859645

Transactions

1

Size

199 B

Version

2

Bits

09dc11ae

Nonce

169,430

Timestamp

9/26/2013, 11:09:35 PM

Confirmations

6,621,384

Mined by

⛏️ P2SHAcGNiyYTPz6cQN38Hj1LhpaPmzXwvxdZTe

Merkle Root

9ef31e8290b4744cce10db7ec79f8ddbde075842020cf7da8e4d704a78ec5d35
Transactions (1)
Coinbase9ef31e8290b474…4d704a78ec5d35
1 in β†’ 1 out10.2700 XPM109 B
AcGNiyYT…XwvxdZTe
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.

7.703 Γ— 10⁹³(94-digit number)
77033016415799178568…78696229670344911999
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
7.703 Γ— 10⁹³(94-digit number)
77033016415799178568…78696229670344911999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.703 Γ— 10⁹³(94-digit number)
77033016415799178568…78696229670344912001
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
1.540 Γ— 10⁹⁴(95-digit number)
15406603283159835713…57392459340689823999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.540 Γ— 10⁹⁴(95-digit number)
15406603283159835713…57392459340689824001
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
3.081 Γ— 10⁹⁴(95-digit number)
30813206566319671427…14784918681379647999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.081 Γ— 10⁹⁴(95-digit number)
30813206566319671427…14784918681379648001
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
6.162 Γ— 10⁹⁴(95-digit number)
61626413132639342855…29569837362759295999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.162 Γ— 10⁹⁴(95-digit number)
61626413132639342855…29569837362759296001
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
1.232 Γ— 10⁹⁡(96-digit number)
12325282626527868571…59139674725518591999
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:57,670,948 XPMΒ·at block #6,803,363 Β· updates every 60s
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