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Block #158,466

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/10/2013, 9:38:58 AM Β· Difficulty 9.8673 Β· 6,648,366 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
773dc8eac87ff1f4e7e86d447eab75427c268742372f9b6c16b3cde0adbedb48
View on Chainz β†—

Height

#158,466

Difficulty

9.867336

Transactions

2

Size

720 B

Version

2

Bits

09de09c0

Nonce

153,643

Timestamp

9/10/2013, 9:38:58 AM

Confirmations

6,648,366

Mined by

⛏️ P2SHAL238g6qUaNSHjwDAQQzED9ccthP8uD33V

Merkle Root

99dedd4a7e10a50dad3bb236849b0820dbe783a82064821c796b761774550bbb
Transactions (2)
Coinbaseefa4f2124fc322…745c509f5eb72e
1 in β†’ 1 out10.2700 XPM109 B
AL238g6q…hP8uD33V
0f558110fdc3f7…9e58bb2bf84d6e
3 in β†’ 2 out30.3100 XPM521 B
AWj8vqaT…rByoonvBAJ3JGyLG…GDAvt5Lf
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.

9.929 Γ— 10⁹⁴(95-digit number)
99292683682411564441…80716266133117829119
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
9.929 Γ— 10⁹⁴(95-digit number)
99292683682411564441…80716266133117829119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.929 Γ— 10⁹⁴(95-digit number)
99292683682411564441…80716266133117829121
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
1.985 Γ— 10⁹⁡(96-digit number)
19858536736482312888…61432532266235658239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.985 Γ— 10⁹⁡(96-digit number)
19858536736482312888…61432532266235658241
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
3.971 Γ— 10⁹⁡(96-digit number)
39717073472964625776…22865064532471316479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.971 Γ— 10⁹⁡(96-digit number)
39717073472964625776…22865064532471316481
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
7.943 Γ— 10⁹⁡(96-digit number)
79434146945929251552…45730129064942632959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.943 Γ— 10⁹⁡(96-digit number)
79434146945929251552…45730129064942632961
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
1.588 Γ— 10⁹⁢(97-digit number)
15886829389185850310…91460258129885265919
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:57,698,760 XPMΒ·at block #6,806,831 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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