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Block #96,747

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/4/2013, 8:57:02 AM Β· Difficulty 9.2791 Β· 6,719,599 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
921c1d2872430b3d03d9d1ad88d844deb1f12526e88f5a432514017efc426bf0
View on Chainz β†—

Height

#96,747

Difficulty

9.279121

Transactions

1

Size

200 B

Version

2

Bits

09477477

Nonce

410,851

Timestamp

8/4/2013, 8:57:02 AM

Confirmations

6,719,599

Mined by

⛏️ P2SHAXvMMum1Pa5kWMWJFC5uKC4CTEy1ajpFRb

Merkle Root

2b8f78f487f4aa2e192def2e3a1a84b7123e6b52c5916ccb089b13e00e5954b6
Transactions (1)
Coinbase2b8f78f487f4aa…9b13e00e5954b6
1 in β†’ 1 out11.6000 XPM109 B
AXvMMum1…y1ajpFRb
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.

2.504 Γ— 10⁹⁢(97-digit number)
25048589581825829545…78148881824785926319
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
2.504 Γ— 10⁹⁢(97-digit number)
25048589581825829545…78148881824785926319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.504 Γ— 10⁹⁢(97-digit number)
25048589581825829545…78148881824785926321
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
5.009 Γ— 10⁹⁢(97-digit number)
50097179163651659091…56297763649571852639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.009 Γ— 10⁹⁢(97-digit number)
50097179163651659091…56297763649571852641
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
1.001 Γ— 10⁹⁷(98-digit number)
10019435832730331818…12595527299143705279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.001 Γ— 10⁹⁷(98-digit number)
10019435832730331818…12595527299143705281
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
2.003 Γ— 10⁹⁷(98-digit number)
20038871665460663636…25191054598287410559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.003 Γ— 10⁹⁷(98-digit number)
20038871665460663636…25191054598287410561
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
4.007 Γ— 10⁹⁷(98-digit number)
40077743330921327272…50382109196574821119
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:57,774,892 XPMΒ·at block #6,816,345 Β· updates every 60s
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