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Block #1,613,451

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/4/2016, 7:33:16 AM Β· Difficulty 10.5991 Β· 5,229,193 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
cc121e428034fbbffeebae88d4b3f79cd0cf637a7c546825a27a02ec2a8f4464
View on Chainz β†—

Height

#1,613,451

Difficulty

10.599067

Transactions

1

Size

199 B

Version

2

Bits

0a995c76

Nonce

381,611,752

Timestamp

6/4/2016, 7:33:16 AM

Confirmations

5,229,193

Mined by

⛏️ P2SHAZvELj9s4U7fUDxD1WkaDSpNutj312Pu5U

Merkle Root

8c6afaba6a75499654e489a65eb5f322f3c4658f18e0467eb6bd50b1046d2f5d
Transactions (1)
Coinbase8c6afaba6a7549…bd50b1046d2f5d
1 in β†’ 1 out8.8900 XPM110 B
AZvELj9s…j312Pu5U
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.

1.490 Γ— 10⁹²(93-digit number)
14907995595080225788…56054940725590904089
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
1.490 Γ— 10⁹²(93-digit number)
14907995595080225788…56054940725590904089
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.490 Γ— 10⁹²(93-digit number)
14907995595080225788…56054940725590904091
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
2.981 Γ— 10⁹²(93-digit number)
29815991190160451576…12109881451181808179
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.981 Γ— 10⁹²(93-digit number)
29815991190160451576…12109881451181808181
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
5.963 Γ— 10⁹²(93-digit number)
59631982380320903152…24219762902363616359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.963 Γ— 10⁹²(93-digit number)
59631982380320903152…24219762902363616361
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
1.192 Γ— 10⁹³(94-digit number)
11926396476064180630…48439525804727232719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.192 Γ— 10⁹³(94-digit number)
11926396476064180630…48439525804727232721
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
2.385 Γ— 10⁹³(94-digit number)
23852792952128361260…96879051609454465439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.385 Γ— 10⁹³(94-digit number)
23852792952128361260…96879051609454465441
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,985,586 XPMΒ·at block #6,842,643 Β· updates every 60s
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