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Block #1,169,405

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/25/2015, 6:57:38 AM Β· Difficulty 10.9354 Β· 5,674,311 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
49136eea2dc4d053b88441c54d95cd467dd83a5bbef57a62ee101e46cef30ce5
View on Chainz β†—

Height

#1,169,405

Difficulty

10.935372

Transactions

2

Size

425 B

Version

2

Bits

0aef748f

Nonce

611,730,941

Timestamp

7/25/2015, 6:57:38 AM

Confirmations

5,674,311

Mined by

⛏️ P2SHAY567KueyukhktiK3zr4rRuaHDS3RanhTd

Merkle Root

131d3d26e457ebf698b174222ab3b01dadbf403e65400aaecf4d7634b5171945
Transactions (2)
Coinbased62c562a9b76fc…9a8bf365177f5e
1 in β†’ 1 out8.3650 XPM110 B
AY567Kue…S3RanhTd
bf1b2435638d60…db77cd7e982613
1 in β†’ 2 out28.3123 XPM225 B
AbZz7Usq…BPicF68hAJkJCGh5…YYzvtVeF
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.

1.373 Γ— 10⁹⁴(95-digit number)
13730241197240299686…58851630394365365789
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
1.373 Γ— 10⁹⁴(95-digit number)
13730241197240299686…58851630394365365789
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.373 Γ— 10⁹⁴(95-digit number)
13730241197240299686…58851630394365365791
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
2.746 Γ— 10⁹⁴(95-digit number)
27460482394480599372…17703260788730731579
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.746 Γ— 10⁹⁴(95-digit number)
27460482394480599372…17703260788730731581
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
5.492 Γ— 10⁹⁴(95-digit number)
54920964788961198744…35406521577461463159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.492 Γ— 10⁹⁴(95-digit number)
54920964788961198744…35406521577461463161
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
1.098 Γ— 10⁹⁡(96-digit number)
10984192957792239748…70813043154922926319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.098 Γ— 10⁹⁡(96-digit number)
10984192957792239748…70813043154922926321
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
2.196 Γ— 10⁹⁡(96-digit number)
21968385915584479497…41626086309845852639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.196 Γ— 10⁹⁡(96-digit number)
21968385915584479497…41626086309845852641
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
4.393 Γ— 10⁹⁡(96-digit number)
43936771831168958995…83252172619691705279
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:57,994,099 XPMΒ·at block #6,843,715 Β· updates every 60s
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