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Block #108,693

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/10/2013, 3:29:08 AM Β· Difficulty 9.6548 Β· 6,706,146 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
72fc719e0d01388a8566a3fca0ec16f548e7ce08633298fafd2f07454a0e1322
View on Chainz β†—

Height

#108,693

Difficulty

9.654837

Transactions

1

Size

200 B

Version

2

Bits

09a7a361

Nonce

122,533

Timestamp

8/10/2013, 3:29:08 AM

Confirmations

6,706,146

Mined by

⛏️ P2SHAXvMMum1Pa5kWMWJFC5uKC4CTEy1ajpFRb

Merkle Root

e20ca14060bcc0ada2a87fba037cc8d9f20d8c71640040cf05f06d5f8351108d
Transactions (1)
Coinbasee20ca14060bcc0…f06d5f8351108d
1 in β†’ 1 out10.7100 XPM109 B
AXvMMum1…y1ajpFRb
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.

1.074 Γ— 10⁹⁸(99-digit number)
10743161228213903155…05201372089520143689
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
1.074 Γ— 10⁹⁸(99-digit number)
10743161228213903155…05201372089520143689
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.074 Γ— 10⁹⁸(99-digit number)
10743161228213903155…05201372089520143691
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
2.148 Γ— 10⁹⁸(99-digit number)
21486322456427806310…10402744179040287379
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.148 Γ— 10⁹⁸(99-digit number)
21486322456427806310…10402744179040287381
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
4.297 Γ— 10⁹⁸(99-digit number)
42972644912855612620…20805488358080574759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.297 Γ— 10⁹⁸(99-digit number)
42972644912855612620…20805488358080574761
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
8.594 Γ— 10⁹⁸(99-digit number)
85945289825711225240…41610976716161149519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.594 Γ— 10⁹⁸(99-digit number)
85945289825711225240…41610976716161149521
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
1.718 Γ— 10⁹⁹(100-digit number)
17189057965142245048…83221953432322299039
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,762,795 XPMΒ·at block #6,814,838 Β· updates every 60s
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