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Block #2,163,901

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/17/2017, 2:05:59 AM Β· Difficulty 10.8994 Β· 4,662,772 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6dfebac25361174acd2edf4ee6d5f582ecd9f438bb0daf96fa5873f981ab7c6b
View on Chainz β†—

Height

#2,163,901

Difficulty

10.899366

Transactions

2

Size

5.74 KB

Version

2

Bits

0ae63cd3

Nonce

472,115,825

Timestamp

6/17/2017, 2:05:59 AM

Confirmations

4,662,772

Mined by

⛏️ P2SHAKk6VnCSvUDinGwvn4K83if2re5drqrmdG

Merkle Root

43711d5b7ea47eb3582238a3cdf1ec85e5f4d2296c3a9e83ae8470b770aaeb9e
Transactions (2)
Coinbaseb6c33c1fe4343f…7625098fe11b03
1 in β†’ 1 out8.4600 XPM109 B
AKk6VnCS…5drqrmdG
d5ead258ecf421…0c4b781b9b849c
38 in β†’ 1 out1623.7634 XPM5.54 KB
ATWEJ9g3…u83jXAeR
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.

2.795 Γ— 10⁹⁢(97-digit number)
27954676109967280029…20557533433333171199
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
2.795 Γ— 10⁹⁢(97-digit number)
27954676109967280029…20557533433333171199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.795 Γ— 10⁹⁢(97-digit number)
27954676109967280029…20557533433333171201
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
5.590 Γ— 10⁹⁢(97-digit number)
55909352219934560059…41115066866666342399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.590 Γ— 10⁹⁢(97-digit number)
55909352219934560059…41115066866666342401
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
1.118 Γ— 10⁹⁷(98-digit number)
11181870443986912011…82230133733332684799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.118 Γ— 10⁹⁷(98-digit number)
11181870443986912011…82230133733332684801
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
2.236 Γ— 10⁹⁷(98-digit number)
22363740887973824023…64460267466665369599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.236 Γ— 10⁹⁷(98-digit number)
22363740887973824023…64460267466665369601
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
4.472 Γ— 10⁹⁷(98-digit number)
44727481775947648047…28920534933330739199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.472 Γ— 10⁹⁷(98-digit number)
44727481775947648047…28920534933330739201
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:57,857,532 XPMΒ·at block #6,826,672 Β· updates every 60s
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