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Block #289,447

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/2/2013, 5:13:52 AM Β· Difficulty 9.9885 Β· 6,537,100 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ca3364ebc84b7133ebeaa3334b397721a777636b6ae5459ff2a3ac0c4c2c4f2a
View on Chainz β†—

Height

#289,447

Difficulty

9.988532

Transactions

1

Size

207 B

Version

2

Bits

09fd1075

Nonce

214,943

Timestamp

12/2/2013, 5:13:52 AM

Confirmations

6,537,100

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

c1bd3fe8c149882c1af9ee71d800bb7612a0b3e8b908cc4e7c81300be7d07ccc
Transactions (1)
Coinbasec1bd3fe8c14988…81300be7d07ccc
1 in β†’ 1 out10.0100 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.

1.657 Γ— 10⁹⁢(97-digit number)
16577721598876554581…71696709109708848639
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
1.657 Γ— 10⁹⁢(97-digit number)
16577721598876554581…71696709109708848639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.657 Γ— 10⁹⁢(97-digit number)
16577721598876554581…71696709109708848641
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
3.315 Γ— 10⁹⁢(97-digit number)
33155443197753109163…43393418219417697279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.315 Γ— 10⁹⁢(97-digit number)
33155443197753109163…43393418219417697281
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
6.631 Γ— 10⁹⁢(97-digit number)
66310886395506218326…86786836438835394559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.631 Γ— 10⁹⁢(97-digit number)
66310886395506218326…86786836438835394561
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
1.326 Γ— 10⁹⁷(98-digit number)
13262177279101243665…73573672877670789119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.326 Γ— 10⁹⁷(98-digit number)
13262177279101243665…73573672877670789121
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
2.652 Γ— 10⁹⁷(98-digit number)
26524354558202487330…47147345755341578239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.652 Γ— 10⁹⁷(98-digit number)
26524354558202487330…47147345755341578241
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:57,856,525 XPMΒ·at block #6,826,546 Β· updates every 60s
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