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Block #1,713,293

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/12/2016, 5:45:03 AM Β· Difficulty 10.6477 Β· 5,118,216 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f8ac2364311e7c6c9101be39bcab4d33ae7d1006344613b795915aed04a84573
View on Chainz β†—

Height

#1,713,293

Difficulty

10.647721

Transactions

1

Size

242 B

Version

2

Bits

0aa5d107

Nonce

31,106,858

Timestamp

8/12/2016, 5:45:03 AM

Confirmations

5,118,216

Mined by

⛏️ P2SHAMeY5ZrV7AqtjFwPLjnwr3BDd53veG96Ko

Merkle Root

0651779c50c73f9293e5221f172339189f6112742c2beb6c13864b6e4190e428
Transactions (1)
Coinbase0651779c50c73f…864b6e4190e428
1 in β†’ 2 out8.8100 XPM152 B
AMeY5ZrV…3veG96KoALPu3s2c…EJXLjVFh
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.

6.625 Γ— 10⁹⁴(95-digit number)
66258342762805675433…14859487939114948799
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
6.625 Γ— 10⁹⁴(95-digit number)
66258342762805675433…14859487939114948799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.625 Γ— 10⁹⁴(95-digit number)
66258342762805675433…14859487939114948801
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
1.325 Γ— 10⁹⁡(96-digit number)
13251668552561135086…29718975878229897599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.325 Γ— 10⁹⁡(96-digit number)
13251668552561135086…29718975878229897601
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
2.650 Γ— 10⁹⁡(96-digit number)
26503337105122270173…59437951756459795199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.650 Γ— 10⁹⁡(96-digit number)
26503337105122270173…59437951756459795201
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
5.300 Γ— 10⁹⁡(96-digit number)
53006674210244540346…18875903512919590399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.300 Γ— 10⁹⁡(96-digit number)
53006674210244540346…18875903512919590401
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
1.060 Γ— 10⁹⁢(97-digit number)
10601334842048908069…37751807025839180799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.060 Γ— 10⁹⁢(97-digit number)
10601334842048908069…37751807025839180801
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:57,896,161 XPMΒ·at block #6,831,508 Β· updates every 60s
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