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Block #82,894

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/25/2013, 6:18:46 PM Β· Difficulty 9.2725 Β· 6,723,418 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f8adc9796a4b3096d40c1c37b35a281d6abc7f5813680176ce23f46d4a634e29
View on Chainz β†—

Height

#82,894

Difficulty

9.272508

Transactions

1

Size

197 B

Version

2

Bits

0945c313

Nonce

284

Timestamp

7/25/2013, 6:18:46 PM

Confirmations

6,723,418

Mined by

⛏️ P2SHAVs8H8b1fbv3283weEWCfJSQvKHyi4s6Cb

Merkle Root

70cf17e52243bff68d700e45ae4aa46ffa42658625c860dcd388f98cf0daea0e
Transactions (1)
Coinbase70cf17e52243bf…88f98cf0daea0e
1 in β†’ 1 out11.6100 XPM110 B
AVs8H8b1…Hyi4s6Cb
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.

1.137 Γ— 10⁸⁷(88-digit number)
11370819720010551713…19267765838073880799
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
1.137 Γ— 10⁸⁷(88-digit number)
11370819720010551713…19267765838073880799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.137 Γ— 10⁸⁷(88-digit number)
11370819720010551713…19267765838073880801
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
2.274 Γ— 10⁸⁷(88-digit number)
22741639440021103427…38535531676147761599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.274 Γ— 10⁸⁷(88-digit number)
22741639440021103427…38535531676147761601
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
4.548 Γ— 10⁸⁷(88-digit number)
45483278880042206854…77071063352295523199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.548 Γ— 10⁸⁷(88-digit number)
45483278880042206854…77071063352295523201
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
9.096 Γ— 10⁸⁷(88-digit number)
90966557760084413709…54142126704591046399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.096 Γ— 10⁸⁷(88-digit number)
90966557760084413709…54142126704591046401
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
1.819 Γ— 10⁸⁸(89-digit number)
18193311552016882741…08284253409182092799
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:57,694,584 XPMΒ·at block #6,806,311 Β· updates every 60s
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