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Block #120,800

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/17/2013, 10:03:18 AM Β· Difficulty 9.7510 Β· 6,675,541 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a8af0e10721dedc2ba98ca9c1a89f292e3d8cbbb72e6b756f2c673240bc57451
View on Chainz β†—

Height

#120,800

Difficulty

9.750963

Transactions

2

Size

1.45 KB

Version

2

Bits

09c03f15

Nonce

264,342

Timestamp

8/17/2013, 10:03:18 AM

Confirmations

6,675,541

Mined by

⛏️ P2SHAMwwgSi4gVEy76GmWninhukHxQP9M9w46X

Merkle Root

2cfb421541b6ed161a567dbf76e00e6b90c1ca885581a8ce1a3bab71f680ef98
Transactions (2)
Coinbase6bf967f1b4b5b9…9e971b48a5786b
1 in β†’ 1 out10.5200 XPM109 B
AMwwgSi4…P9M9w46X
8306bee8672bbe…320c90acfcea97
10 in β†’ 1 out73.6400 XPM1.26 KB
AR9hPx16…hbPLeD3K
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.

1.580 Γ— 10⁹⁸(99-digit number)
15800568631358005306…96501655927034469099
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
1.580 Γ— 10⁹⁸(99-digit number)
15800568631358005306…96501655927034469099
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.580 Γ— 10⁹⁸(99-digit number)
15800568631358005306…96501655927034469101
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
3.160 Γ— 10⁹⁸(99-digit number)
31601137262716010612…93003311854068938199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.160 Γ— 10⁹⁸(99-digit number)
31601137262716010612…93003311854068938201
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
6.320 Γ— 10⁹⁸(99-digit number)
63202274525432021225…86006623708137876399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.320 Γ— 10⁹⁸(99-digit number)
63202274525432021225…86006623708137876401
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
1.264 Γ— 10⁹⁹(100-digit number)
12640454905086404245…72013247416275752799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.264 Γ— 10⁹⁹(100-digit number)
12640454905086404245…72013247416275752801
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
2.528 Γ— 10⁹⁹(100-digit number)
25280909810172808490…44026494832551505599
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:57,614,720 XPMΒ·at block #6,796,340 Β· updates every 60s
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