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Block #150,096

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/4/2013, 7:25:17 PM Β· Difficulty 9.8584 Β· 6,645,853 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0d808ef98c18c709cc2dd3c799cad3a6c1a70e307461fd3407d1454dd7dd6f01
View on Chainz β†—

Height

#150,096

Difficulty

9.858431

Transactions

2

Size

1.83 KB

Version

2

Bits

09dbc21e

Nonce

197,856

Timestamp

9/4/2013, 7:25:17 PM

Confirmations

6,645,853

Mined by

⛏️ P2SHAJa98wvS97hkzbU6mF9XmavceJadArRYvJ

Merkle Root

110b7a9f0c14ebb835619fb5a16859f8dcbe58e387a560d0455dfcac7c3023b1
Transactions (2)
Coinbaseed8141a2babdc1…c812f9a53bd129
1 in β†’ 1 out10.2900 XPM109 B
AJa98wvS…adArRYvJ
58353ec9a0b302…b6b6a460fed8c3
14 in β†’ 2 out144.3200 XPM1.63 KB
ARNQBY4k…PDEd5qMiAdrZgAo5…aLTu4NiJ
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.

4.503 Γ— 10⁹⁢(97-digit number)
45039513912299593782…70246596659301032639
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
4.503 Γ— 10⁹⁢(97-digit number)
45039513912299593782…70246596659301032639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.503 Γ— 10⁹⁢(97-digit number)
45039513912299593782…70246596659301032641
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
9.007 Γ— 10⁹⁢(97-digit number)
90079027824599187565…40493193318602065279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.007 Γ— 10⁹⁢(97-digit number)
90079027824599187565…40493193318602065281
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
1.801 Γ— 10⁹⁷(98-digit number)
18015805564919837513…80986386637204130559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.801 Γ— 10⁹⁷(98-digit number)
18015805564919837513…80986386637204130561
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
3.603 Γ— 10⁹⁷(98-digit number)
36031611129839675026…61972773274408261119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.603 Γ— 10⁹⁷(98-digit number)
36031611129839675026…61972773274408261121
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
7.206 Γ— 10⁹⁷(98-digit number)
72063222259679350052…23945546548816522239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.206 Γ— 10⁹⁷(98-digit number)
72063222259679350052…23945546548816522241
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
1.441 Γ— 10⁹⁸(99-digit number)
14412644451935870010…47891093097633044479
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,611,681 XPMΒ·at block #6,795,948 Β· updates every 60s
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