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Block #1,895,066

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/15/2016, 9:32:21 AM Β· Difficulty 10.7477 Β· 4,922,781 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8175921b03d53e73f3602e58c50cd6b309376c3f9a88d622385ce42362861473
View on Chainz β†—

Height

#1,895,066

Difficulty

10.747686

Transactions

2

Size

874 B

Version

2

Bits

0abf6859

Nonce

1,171,716,701

Timestamp

12/15/2016, 9:32:21 AM

Confirmations

4,922,781

Mined by

⛏️ P2SHAZHCGDW4PJgEu6yRzRkz9PwrH5GZ6p2Lch

Merkle Root

2cf2ff6a00924db4fe3d238ea7a4e57f5f15c11fc059a7898cb1952bcb17a610
Transactions (2)
Coinbaseb2abba1b326c69…24ea4c78ed8b72
1 in β†’ 1 out8.6500 XPM110 B
AZHCGDW4…GZ6p2Lch
af49f4c98fe258…1348fcb63bf25c
4 in β†’ 2 out5.5145 XPM673 B
ASMMZz4E…7FeHYYcpAMo9kVVL…zUKYDfXn
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.

8.244 Γ— 10⁹⁡(96-digit number)
82449676563792585084…94778618184679260159
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
8.244 Γ— 10⁹⁡(96-digit number)
82449676563792585084…94778618184679260159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.244 Γ— 10⁹⁡(96-digit number)
82449676563792585084…94778618184679260161
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
1.648 Γ— 10⁹⁢(97-digit number)
16489935312758517016…89557236369358520319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.648 Γ— 10⁹⁢(97-digit number)
16489935312758517016…89557236369358520321
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
3.297 Γ— 10⁹⁢(97-digit number)
32979870625517034033…79114472738717040639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.297 Γ— 10⁹⁢(97-digit number)
32979870625517034033…79114472738717040641
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
6.595 Γ— 10⁹⁢(97-digit number)
65959741251034068067…58228945477434081279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.595 Γ— 10⁹⁢(97-digit number)
65959741251034068067…58228945477434081281
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
1.319 Γ— 10⁹⁷(98-digit number)
13191948250206813613…16457890954868162559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.319 Γ— 10⁹⁷(98-digit number)
13191948250206813613…16457890954868162561
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:57,786,841 XPMΒ·at block #6,817,846 Β· updates every 60s
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