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Block #276,491

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/27/2013, 5:09:44 AM Β· Difficulty 9.9633 Β· 6,531,755 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
337f4402d0d2fe6bcfa4294d59d0c18fd8fadfe12adc2e00fccd56db11c005f6
View on Chainz β†—

Height

#276,491

Difficulty

9.963303

Transactions

1

Size

201 B

Version

2

Bits

09f69b0c

Nonce

49,435

Timestamp

11/27/2013, 5:09:44 AM

Confirmations

6,531,755

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

b7e427564ac1e461dd2507c5758288dd1a83e4e3ab3359e94e82d854687f1f6b
Transactions (1)
Coinbaseb7e427564ac1e4…82d854687f1f6b
1 in β†’ 1 out10.0600 XPM109 B
AeKNrjNj…1NEq95Ta
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.

1.622 Γ— 10⁹⁹(100-digit number)
16222482469029623712…57524367055142256639
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
1.622 Γ— 10⁹⁹(100-digit number)
16222482469029623712…57524367055142256639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.622 Γ— 10⁹⁹(100-digit number)
16222482469029623712…57524367055142256641
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
3.244 Γ— 10⁹⁹(100-digit number)
32444964938059247424…15048734110284513279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.244 Γ— 10⁹⁹(100-digit number)
32444964938059247424…15048734110284513281
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
6.488 Γ— 10⁹⁹(100-digit number)
64889929876118494849…30097468220569026559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.488 Γ— 10⁹⁹(100-digit number)
64889929876118494849…30097468220569026561
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
1.297 Γ— 10¹⁰⁰(101-digit number)
12977985975223698969…60194936441138053119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.297 Γ— 10¹⁰⁰(101-digit number)
12977985975223698969…60194936441138053121
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
2.595 Γ— 10¹⁰⁰(101-digit number)
25955971950447397939…20389872882276106239
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:57,710,015 XPMΒ·at block #6,808,245 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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