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Block #1,972,006

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/6/2017, 6:38:09 PM Β· Difficulty 10.7542 Β· 4,845,457 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
168b8df3456851105e5e513359fbb046445a74017b1484d3497639806f648b6c
View on Chainz β†—

Height

#1,972,006

Difficulty

10.754189

Transactions

2

Size

869 B

Version

2

Bits

0ac11283

Nonce

146,749,725

Timestamp

2/6/2017, 6:38:09 PM

Confirmations

4,845,457

Mined by

⛏️ P2SHAL7Svbb7QcqyQgPAi8jB6LtQikhwrC3Z7U

Merkle Root

5bc4954e04f1a12034f0ac41959c30c5ffe40be049a6382e515ae79ef7173a5a
Transactions (2)
Coinbasea2e0509f6b14d6…34a374dc4643b0
1 in β†’ 1 out8.6400 XPM110 B
AL7Svbb7…hwrC3Z7U
cb6633b35c401e…47a9681d09818f
4 in β†’ 2 out1.0390 XPM668 B
Aa2TtTcT…tLWhEDFoALKwtKu5…L1Sizeka
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.

1.475 Γ— 10⁹⁷(98-digit number)
14753579462044847620…85364052170376417279
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
1.475 Γ— 10⁹⁷(98-digit number)
14753579462044847620…85364052170376417279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.475 Γ— 10⁹⁷(98-digit number)
14753579462044847620…85364052170376417281
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
2.950 Γ— 10⁹⁷(98-digit number)
29507158924089695241…70728104340752834559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.950 Γ— 10⁹⁷(98-digit number)
29507158924089695241…70728104340752834561
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
5.901 Γ— 10⁹⁷(98-digit number)
59014317848179390482…41456208681505669119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.901 Γ— 10⁹⁷(98-digit number)
59014317848179390482…41456208681505669121
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
1.180 Γ— 10⁹⁸(99-digit number)
11802863569635878096…82912417363011338239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.180 Γ— 10⁹⁸(99-digit number)
11802863569635878096…82912417363011338241
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
2.360 Γ— 10⁹⁸(99-digit number)
23605727139271756193…65824834726022676479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.360 Γ— 10⁹⁸(99-digit number)
23605727139271756193…65824834726022676481
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:57,783,754 XPMΒ·at block #6,817,462 Β· updates every 60s
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