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Block #1,347,203

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/29/2015, 9:07:04 AM Β· Difficulty 10.8248 Β· 5,461,775 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f09269b3706f899c6b5b087e37c7d5073769ecbc7b37708a28584f2c67d81d11
View on Chainz β†—

Height

#1,347,203

Difficulty

10.824819

Transactions

3

Size

3.81 KB

Version

2

Bits

0ad32758

Nonce

1,628,525,086

Timestamp

11/29/2015, 9:07:04 AM

Confirmations

5,461,775

Mined by

⛏️ P2SHAbVKoJEokkx6peCTsvWsokEwFajBC8U1Y3

Merkle Root

818833f9e140ee82768fbc0790d32d6fa36e8c30450abb3545a900ab7043c718
Transactions (3)
Coinbase01a8b84e753f19…6e15cf7ab80d6e
1 in β†’ 1 out8.5700 XPM110 B
AbVKoJEo…jBC8U1Y3
95854fd835e851…45a04fdd84a967
18 in β†’ 2 out49.7245 XPM2.68 KB
AbecWDS9…1vtToSMLATBSmj3H…2vht6bd1
db12fc80179ab0…c6f3af92524a92
6 in β†’ 2 out500.0101 XPM964 B
AJjnK9uC…VreFquR4APnYb3E2…MkgRtv28
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.

1.381 Γ— 10⁹⁴(95-digit number)
13813723468072179821…00307341414812130879
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
1.381 Γ— 10⁹⁴(95-digit number)
13813723468072179821…00307341414812130879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.381 Γ— 10⁹⁴(95-digit number)
13813723468072179821…00307341414812130881
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
2.762 Γ— 10⁹⁴(95-digit number)
27627446936144359642…00614682829624261759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.762 Γ— 10⁹⁴(95-digit number)
27627446936144359642…00614682829624261761
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
5.525 Γ— 10⁹⁴(95-digit number)
55254893872288719284…01229365659248523519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.525 Γ— 10⁹⁴(95-digit number)
55254893872288719284…01229365659248523521
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
1.105 Γ— 10⁹⁡(96-digit number)
11050978774457743856…02458731318497047039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.105 Γ— 10⁹⁡(96-digit number)
11050978774457743856…02458731318497047041
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
2.210 Γ— 10⁹⁡(96-digit number)
22101957548915487713…04917462636994094079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.210 Γ— 10⁹⁡(96-digit number)
22101957548915487713…04917462636994094081
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:57,715,880 XPMΒ·at block #6,808,977 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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