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Block #2,096,557

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/2/2017, 1:55:45 AM Β· Difficulty 10.8724 Β· 4,740,037 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
313f1b8b30bac3cd1b66e5fb77877b123259eca248a0d117fdc6a95ce0cde959
View on Chainz β†—

Height

#2,096,557

Difficulty

10.872395

Transactions

2

Size

1.10 KB

Version

2

Bits

0adf554c

Nonce

651,539,085

Timestamp

5/2/2017, 1:55:45 AM

Confirmations

4,740,037

Mined by

⛏️ P2SHAWfybs4wtwB5HAeUVpMCBWVBw3qmp15ow2

Merkle Root

ad7ceda39196c95b91bc422c746bee322f8fa314544b428f920dd45b3544edff
Transactions (2)
Coinbase50c73e9317e36a…e887aa2e0a98cd
1 in β†’ 1 out8.4800 XPM110 B
AWfybs4w…qmp15ow2
3bb47dc512df9d…82ddf3c3968b2d
6 in β†’ 1 out5007.9244 XPM929 B
AHKEqLWG…Z6JsKv41
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.

5.769 Γ— 10⁹³(94-digit number)
57696302996386795991…34737515479862169599
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
5.769 Γ— 10⁹³(94-digit number)
57696302996386795991…34737515479862169599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.769 Γ— 10⁹³(94-digit number)
57696302996386795991…34737515479862169601
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
1.153 Γ— 10⁹⁴(95-digit number)
11539260599277359198…69475030959724339199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.153 Γ— 10⁹⁴(95-digit number)
11539260599277359198…69475030959724339201
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
2.307 Γ— 10⁹⁴(95-digit number)
23078521198554718396…38950061919448678399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.307 Γ— 10⁹⁴(95-digit number)
23078521198554718396…38950061919448678401
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
4.615 Γ— 10⁹⁴(95-digit number)
46157042397109436792…77900123838897356799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.615 Γ— 10⁹⁴(95-digit number)
46157042397109436792…77900123838897356801
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
9.231 Γ— 10⁹⁴(95-digit number)
92314084794218873585…55800247677794713599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.231 Γ— 10⁹⁴(95-digit number)
92314084794218873585…55800247677794713601
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
1.846 Γ— 10⁹⁡(96-digit number)
18462816958843774717…11600495355589427199
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,937,022 XPMΒ·at block #6,836,593 Β· updates every 60s
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