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Block #1,719,151

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/16/2016, 1:43:02 AM Β· Difficulty 10.6711 Β· 5,076,421 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
085c5b72c08e7631feabc2ada6c01fc4a28961494fd7f41b0ad4034a322e2660
View on Chainz β†—

Height

#1,719,151

Difficulty

10.671071

Transactions

1

Size

243 B

Version

2

Bits

0aabcb52

Nonce

7,313,435

Timestamp

8/16/2016, 1:43:02 AM

Confirmations

5,076,421

Mined by

⛏️ P2SHAKjaKd2Kxt1buNBYuJDadjFL1cDPsqUE8e

Merkle Root

c274c0d276964b462443b3c679b2a9dd03feab1eb556a68533f74a60e2d5de3e
Transactions (1)
Coinbasec274c0d276964b…f74a60e2d5de3e
1 in β†’ 2 out8.7700 XPM152 B
AKjaKd2K…DPsqUE8eAXbk7f7A…Tx7JECPG
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.

4.451 Γ— 10⁹⁢(97-digit number)
44514425036918319793…76349643105252147199
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
4.451 Γ— 10⁹⁢(97-digit number)
44514425036918319793…76349643105252147199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.451 Γ— 10⁹⁢(97-digit number)
44514425036918319793…76349643105252147201
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
8.902 Γ— 10⁹⁢(97-digit number)
89028850073836639587…52699286210504294399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.902 Γ— 10⁹⁢(97-digit number)
89028850073836639587…52699286210504294401
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
1.780 Γ— 10⁹⁷(98-digit number)
17805770014767327917…05398572421008588799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.780 Γ— 10⁹⁷(98-digit number)
17805770014767327917…05398572421008588801
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
3.561 Γ— 10⁹⁷(98-digit number)
35611540029534655835…10797144842017177599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.561 Γ— 10⁹⁷(98-digit number)
35611540029534655835…10797144842017177601
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
7.122 Γ— 10⁹⁷(98-digit number)
71223080059069311670…21594289684034355199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.122 Γ— 10⁹⁷(98-digit number)
71223080059069311670…21594289684034355201
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:57,608,636 XPMΒ·at block #6,795,571 Β· updates every 60s
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