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Block #104,721

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/8/2013, 4:40:45 AM Β· Difficulty 9.5646 Β· 6,721,714 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
08d9f341ca279752e08f97365277b2e1c4799a3d8431d09cc911ab382d78f8ea
View on Chainz β†—

Height

#104,721

Difficulty

9.564588

Transactions

1

Size

200 B

Version

2

Bits

099088d5

Nonce

33,482

Timestamp

8/8/2013, 4:40:45 AM

Confirmations

6,721,714

Mined by

⛏️ P2SHAeEXQxqG1a9HUoHobjrNQ1M2oHJ2q5dxWc

Merkle Root

b4d3a09e1d6d1526aad5cda49c5711d4cf4603ea459dd4556ed771f5ea6fa388
Transactions (1)
Coinbaseb4d3a09e1d6d15…d771f5ea6fa388
1 in β†’ 1 out10.9200 XPM109 B
AeEXQxqG…J2q5dxWc
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.

3.302 Γ— 10⁹⁢(97-digit number)
33020293270793256129…28111567978201425459
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
3.302 Γ— 10⁹⁢(97-digit number)
33020293270793256129…28111567978201425459
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.302 Γ— 10⁹⁢(97-digit number)
33020293270793256129…28111567978201425461
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
6.604 Γ— 10⁹⁢(97-digit number)
66040586541586512258…56223135956402850919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.604 Γ— 10⁹⁢(97-digit number)
66040586541586512258…56223135956402850921
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
1.320 Γ— 10⁹⁷(98-digit number)
13208117308317302451…12446271912805701839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.320 Γ— 10⁹⁷(98-digit number)
13208117308317302451…12446271912805701841
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
2.641 Γ— 10⁹⁷(98-digit number)
26416234616634604903…24892543825611403679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.641 Γ— 10⁹⁷(98-digit number)
26416234616634604903…24892543825611403681
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
5.283 Γ— 10⁹⁷(98-digit number)
52832469233269209806…49785087651222807359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.283 Γ— 10⁹⁷(98-digit number)
52832469233269209806…49785087651222807361
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:57,855,617 XPMΒ·at block #6,826,434 Β· updates every 60s
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