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Block #1,680,982

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/20/2016, 2:04:17 AM Β· Difficulty 10.7119 Β· 5,158,550 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
474fdbf7f9de57e4f546d8984898b18963c857c84ea2dfdbe1da94e7a5d81786
View on Chainz β†—

Height

#1,680,982

Difficulty

10.711856

Transactions

1

Size

200 B

Version

2

Bits

0ab63c30

Nonce

866,192,670

Timestamp

7/20/2016, 2:04:17 AM

Confirmations

5,158,550

Mined by

⛏️ P2SHALqh8QwBc32crPS7vfg2xLnJ65MtUppofW

Merkle Root

aedb863e4deaea2c440bcee077412e440f4e49b0c270bbdb0b75e223183ceb3f
Transactions (1)
Coinbaseaedb863e4deaea…75e223183ceb3f
1 in β†’ 1 out8.7000 XPM109 B
ALqh8QwB…MtUppofW
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.

1.412 Γ— 10⁹⁢(97-digit number)
14124445813861159381…53876488927107932159
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
1.412 Γ— 10⁹⁢(97-digit number)
14124445813861159381…53876488927107932159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.412 Γ— 10⁹⁢(97-digit number)
14124445813861159381…53876488927107932161
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
2.824 Γ— 10⁹⁢(97-digit number)
28248891627722318762…07752977854215864319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.824 Γ— 10⁹⁢(97-digit number)
28248891627722318762…07752977854215864321
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
5.649 Γ— 10⁹⁢(97-digit number)
56497783255444637524…15505955708431728639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.649 Γ— 10⁹⁢(97-digit number)
56497783255444637524…15505955708431728641
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
1.129 Γ— 10⁹⁷(98-digit number)
11299556651088927504…31011911416863457279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.129 Γ— 10⁹⁷(98-digit number)
11299556651088927504…31011911416863457281
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
2.259 Γ— 10⁹⁷(98-digit number)
22599113302177855009…62023822833726914559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.259 Γ— 10⁹⁷(98-digit number)
22599113302177855009…62023822833726914561
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:57,960,546 XPMΒ·at block #6,839,531 Β· updates every 60s
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