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Block #159,856

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/11/2013, 11:28:11 AM Β· Difficulty 9.8631 Β· 6,650,055 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3e1f5f6d532a0c88e9090c7759a49acf053c977693d6ba45a4352f1448c21f86
View on Chainz β†—

Height

#159,856

Difficulty

9.863103

Transactions

2

Size

355 B

Version

2

Bits

09dcf452

Nonce

31,269

Timestamp

9/11/2013, 11:28:11 AM

Confirmations

6,650,055

Mined by

⛏️ P2SHAM9R37qPciuhUNYvwcMUHTUsnwhm8dCX8m

Merkle Root

4882e62abc52ea352493678e5bb1d5feebc79bae0fde3a8ff78b1ee0259f9b4a
Transactions (2)
Coinbasefde24c79dfda54…6df8b3503edd9d
1 in β†’ 1 out10.2700 XPM109 B
AM9R37qP…hm8dCX8m
288ed6f2495207…4769d5e9a6bbea
1 in β†’ 1 out10.2400 XPM157 B
AJRwGPSP…QDRWdi2B
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.

1.286 Γ— 10⁹³(94-digit number)
12860780814597245140…00751503745022868909
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
1.286 Γ— 10⁹³(94-digit number)
12860780814597245140…00751503745022868909
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.286 Γ— 10⁹³(94-digit number)
12860780814597245140…00751503745022868911
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
2.572 Γ— 10⁹³(94-digit number)
25721561629194490281…01503007490045737819
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.572 Γ— 10⁹³(94-digit number)
25721561629194490281…01503007490045737821
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
5.144 Γ— 10⁹³(94-digit number)
51443123258388980562…03006014980091475639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.144 Γ— 10⁹³(94-digit number)
51443123258388980562…03006014980091475641
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
1.028 Γ— 10⁹⁴(95-digit number)
10288624651677796112…06012029960182951279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.028 Γ— 10⁹⁴(95-digit number)
10288624651677796112…06012029960182951281
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
2.057 Γ— 10⁹⁴(95-digit number)
20577249303355592224…12024059920365902559
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:57,723,372 XPMΒ·at block #6,809,910 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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