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Block #273,134

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/25/2013, 3:38:38 PM Β· Difficulty 9.9542 Β· 6,540,760 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e065ed493f543dd7193c7aa2e3917268a9fd614b20ca8e66368afbff666a5283
View on Chainz β†—

Height

#273,134

Difficulty

9.954171

Transactions

1

Size

208 B

Version

2

Bits

09f44491

Nonce

67,983

Timestamp

11/25/2013, 3:38:38 PM

Confirmations

6,540,760

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

29ad325ba80e80e81f03e79d0ededaa3e2cd2aa456e90d2861c7fb1dbae1805a
Transactions (1)
Coinbase29ad325ba80e80…c7fb1dbae1805a
1 in β†’ 1 out10.0800 XPM116 B
AcLBm5Z9…S683d7c3
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.

3.695 Γ— 10⁹⁹(100-digit number)
36956207939968487652…82060676888295837499
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
3.695 Γ— 10⁹⁹(100-digit number)
36956207939968487652…82060676888295837499
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.695 Γ— 10⁹⁹(100-digit number)
36956207939968487652…82060676888295837501
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
7.391 Γ— 10⁹⁹(100-digit number)
73912415879936975304…64121353776591674999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.391 Γ— 10⁹⁹(100-digit number)
73912415879936975304…64121353776591675001
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
1.478 Γ— 10¹⁰⁰(101-digit number)
14782483175987395060…28242707553183349999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.478 Γ— 10¹⁰⁰(101-digit number)
14782483175987395060…28242707553183350001
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
2.956 Γ— 10¹⁰⁰(101-digit number)
29564966351974790121…56485415106366699999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.956 Γ— 10¹⁰⁰(101-digit number)
29564966351974790121…56485415106366700001
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
5.912 Γ— 10¹⁰⁰(101-digit number)
59129932703949580243…12970830212733399999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.912 Γ— 10¹⁰⁰(101-digit number)
59129932703949580243…12970830212733400001
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:57,755,229 XPMΒ·at block #6,813,893 Β· updates every 60s
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